STRESS STRAIN CURVES UNDER COMPRESSION FOR CMSX4...

ADVANCES IN MANUFACTURING SCIENCE AND TECHNOLOGY

Vol. 38, No. 3, 2014

DOI: 10.2478/amst-2014-0019

Address: Andrzej NOWOTNIK PhD Eng., Paweł PĘDRAK, MSc Eng., Paweł ROKICKI, PhD Eng., Grażyna MRÓWKA-NOWOTNIK, DSc Eng., Prof. Jan SIENIAWSKI, Rzeszow University of Technology, Department of Materials Science, 2 W. Pola St., 35-959 Rzeszów, Phone (+48, 0-17) 865 11 24, Fax (+48, 0-17) 854 48 32, E-mail: [email protected]

STRESS–STRAIN CURVES UNDER COMPRESSION

FOR CMSX4 NICKEL BASED SUPERALLOY

Andrzej Nowotnik, Paweł Pędrak, Paweł Rokicki,

Grażyna Mrówka-Nowotnik, Jan Sieniawski

S u m m a r y

Variations of a flow stress vs. true strain illustrate behavior of material during plastic deformation. Stress-strain relationship is generally evaluated by a torsion, compression and tensile tests. Results of these tests provide crucial information pertaining to the stress values which are necessary to run deformation process at specified deformation parameters. Uniaxial compression tests at the temperature through which precipitation hardening phases process occurred (900-1200°C), were conducted on superalloy – CMSX-4, to study the effect of temperature and strain rate (

=10-4

and 4x10-4

s-1

) on its flow stress. On the basis of received flow stress values activation energy of a high-temperature deformation process was estimated. Mathematical dependences (pl – T i pl –

) and compression data were used to determine material’s constants. These constants allow to derive a formula that describes the relationship between strain rate (

), deformation temperature (T) and flow stress pl –

1 exp( / )nA Q RT

.

Keywords: flow stress, plastic deformation, CMSX4, superalloys, activation energy

Krzywe odkształcania nadstopu CMSX-4 po próbie ściskania w wysokiej temperaturze

S t r e s z c z e n i e

Zachowanie się materiału podczas odkształcania plastycznego na gorąco charakteryzują krzywe zmiany naprężenia uplastyczniającego w funkcji odkształcenia. Do ich oceny stosowane są próby skręcania, ściskania lub rozciągania. Pozwalają określić dane niezbędne do prowadzenia procesu przeróbki plastycznej materiału z zastosowaniem odpowiednich parametrów odkształcania – temperatury i prędkości chłodzenia. W pracy przedstawiono analizę wyników badań wpływu temperatury i prędkości odkształcania (

=10-4

i 4x10-4

s-1

) na wartość naprężenia uplastyczniającego nadstopu niklu – CMSX-4 w zakresie wartości temperatury wydzielania cząstek faz umacniających (900-1200°C) uzyskane w jednoosiowej próbie ściskania. Ustalone wartości naprężenia uplastyczniającego były podstawą do wyznaczenia energii aktywacji Q procesu odkształcania wysokotemperaturowego. Na podstawie uzyskanych danych oraz odpowiednich zależności (pl – T i pl –

) określono wartości stałych materiałowych oraz ustalono zależność prędkości (

), temperatury odkształcenia (T) i naprężeniem ustalonego płynięcia plastycznego pl - 1 exp( / )nA Q RT

.

Słowa kluczowe: krzywe płynięcia, odkształcenie plastyczne, nadstopy niklu, CMSX4, energia aktywacji

66 A. Nowotnik, P. Pędrak, P. Rokicki, G. Mrówka-Nowotnik, J. Sieniawski

1. Introduction

With their many exceptional properties, CMSX-4 has a high potential to

become important high-temperature structural material. CMSX-4 is Ni-based

alloy. Nickel based superalloys CMSX-4 is extensively used in aero gas turbine

for critical assemblies such as discs and shafts which are subjected to severe

service conditions at high temperature. The need of thermomechanical

processing of superalloys for higher properties is known and published by

mainly for forged products. There is lack information for the alloys subjected to

deformation at high temperature under dynamic condition. Keeping this in view,

compression testing within temperature characteristic for precipitation of

hardening phases were taken up. This paper reports mechanical properties of the

deformed CMSX-4.

One of the principal aim of a modern materials engineering is to prepare for

each, as regard a chemical composition, type of superalloy potentially universal

mechanical characteristic (true stress-true strain curves). These may allow to run

a safe plastic deformation process of given precipitation hardened superalloy and

make possible to predict suitable microstructures from overcooled austenite after

heat treatment with application of various cooling rate, what is to determine final

properties of such superalloy. Subsequently chemical and phase composition,

microstructure and method of deformation or even its parameters play decisive

role in the plastic deformation process. These factors affect a strengthening

kinetics and changes of the microstructure and in the end the mechanical

properties of a material. The hardening due to deformation process is relaxed by

the softening process, namely recovering and (or) recrystallization. It is assumed

that at high deformation temperatures, materials with a high stacking fault

energy (SFE) such as aluminium, nickel etc. dynamic recovery becomes the sole

softening process, however dynamic recrystallization may play significant role

in the softening of deformed materials with a low SFE [1-3].

One of the most fundamental feature that characterize plastic workability of

material is flow stress pl – i.e. stress essential for a plastic flow initiation and

following continuation in a one-dimensional stress state [4]. The flow stress

value is strongly affected by temperature, deformation value, strain rate and the

history of the course of deformation process [5]. To describe the relationship

between of deformation parameters and stress value, following mathematical

formula can be used [6-10]:

Stress–strain curves under compression ... 67

sinh expn Q

ART

(1)

where: A, α, n – material constants,

– effective strain rate, Q – experimental

activation energy for deformation process, T – deformation temperature,

σ – flow stress value (σpl), or stress coressponds to the first maximum at a true

stress/true strain curve (σmax), R – universal gas constant (8,314 J/mol·K).

In the case of the small stresses (ασ) ≤ 0,39; the equation (1) can be

simplified (value of sinh(ασ) can be approximated by ≈ ασ with an accuracy

±1%) and expressed as:

1 expn QA

RT

(2)

where: A1 = Aαn – material constant

For a large value of the flow stress – ασ > 3,9 (sinh (ασ) ≈ 0,5exp(βσ)) the

equation (1) can be modified as follows:

2 exp expQ

ART

(3)

where: A2= A/2n; β = αn

It is known that temperature has a significant effect on the flow stress

variations during hot forming process. In addition, commonly used in

description of high-temperature deformation process, Zener-Holloman parameter

(usually known as a flow stress expressed in terms of temperature-compensated

strain rate or as a deformation intensity) is thought to influence the course of

= f() function, the flow stress value – maximum max and at stationary state

– pl, dynamic recrystallization kinetic and size of dynamically recrystallized

grains.

expQ

ZRT

(4)

An activation energy for deformation process Q (equation (1)-(3)) is

characteristic for an examined material and deformation parameters. In the

practice, the value of Q is constant, and depends on the method of forming

process and deformation parameters [8]. Therefore its value can be used only for


mathematical description of the relation: stress-deformation-temperature. In

general, during hot-deformation of a material with high stacking fault energy (Al

alloys and ferritic Fe alloys) stabilized value of the flow stress results from

softening due to dynamic recovery, Q value is close to the value of activation

energy for the self-diffusion process. For materials with low SFE (Ni, Cu and

stainless steel), in most cases undergoing both dynamic recovery and

recrystallization, Q value exceeds the value of activation energy for the self-

diffusion process [6, 8]. The aim of the research was to obtain empirical

relationship between the flow stress and phase composition and deformation

parameters (deformation temperature, strain rate and cooling during

deformation). The obtained values of a flow stress allow us to estimate

the activation energy for high-deformation process of the examined superalloys

[11-15].

2. Material and experimental

Investigation was carried out on CMSX-4 – chemical composition (wt % ):

Cr – 6.5, Co – 9, Mo – 0.6, W – 6, Ta – 6.5, Ti – 1, Al – 5.6, Hf – 0.1, Fe – 3,

Ni – balance). In order to determine the effect of temperature and strain rate on

flow stress value, isothermal high-temperature compression tests were

performed on computer-controlled, Gleeble test equipment was used for the

compression test (Fig. 1).

Fig. 1. Outline of the hot compression test and measured

parameters in Gleeble thermo mechanical simulator

The cubicoidal samples (20x10x20 mm) were conductive heated to 1150°C

at heating rate of 3°C/s, held for 300 s and finally cooled to the compression

temperature. The temperature was controlled by a type K thermocouple inserted

and welded in an opening hollowed out in the central part of the sample by spark

erosion technique. Three additional thermocouples were used to acquire the

distribution of the temperature from one of the faces to the centre of the

Loa

dcell

Jaw Jaw

Tool (Anvil)

Spe

cim

en

Lubricant Thermocouple


specimen. A combination of graphite and molybdenum foils was used to reduce

the friction between the anvils and the specimen as well as the gradient of

temperature along the specimen. The deformation for all the tests was controlled

by the stroke and measured by means of a loadcells attached to the jaws. The

tests were carried out in an argon atmosphere.

The flow stress values under two different low strain rates over a range of

temperatures (900-1200°C) were measured. The value of activation energy was

determined in the following way:

By finding logarithm the following equation has been obtained:

1ln ln sinhn Q

A TR

(5)

hence:

1

ln Q

T R

(6)

This relation (6) allow us to evaluate the activation energy value for a forming

process carried out at σ = constans, e.g.: creep test. For the processes run at constant

strain rate the equation (6) is rearranging to the following form:

1 1

ln sinhln ln

ln sinh

T

Q

T T R

(7)

hence:

1

ln sinhln

ln sinhT

Q RT

(8)

The value of activation energy can be also estimated by applying following

formula:


1

ln

ln

ln T

TQ

(9)

The effect of deformation temperature on the true stress-true strain curves for the

superalloy after different heat-treatment deformed at each of the two strain rates

(10-4

; 4x10-4

s-1

) and temperature of 900-1200°C is shown in Fig. 2-4.

a) b)

Fig. 2. True stress-true strain curves CMSX-4 deformed at different temperatures and a strain rate

of a) 10–4 s–1 and b) 410–4 s–1 (the deformation temperature was indicated in the figure)

a) b)

Fig. 3. True stress-true strain curves CMSX-4 after solution heat treatment and aged, deformed at

different temperatures and a strain rate of: a) 10–4 s–1 and b) 4·10–4 s–1 (the deformation

temperature was indicated in the figure)


A plot of the change in the peak strain with inverse temperature is shown in

Fig. 5. The slopes of the peak strain and 1/T plots for the CMSX-4 alloy are

approximately equal at higher temperatures and shift to slightly higher values at

1200°C for the alloy deformed at higher strain rate. The same effect was

observed after deformation of CMSX4 after solution heat treatment and both

stage of aging. This change or transition in the slope may be attributed to the

influence of hardened precipitation on dynamic recrystallization.

a) b)

Fig. 4. True stress-true strain curves CMSX-4 after solution heat treatment and two stage of aging,

deformed at different temperatures and a strain rate of: a) 10–4 s–1 and b) 4·10–4 s–1 (the

deformation temperature was indicated in the figure)

a) b)

c)


Fig. 5. Relationship between the flow stress and deformation temperature for CMSX4:

a) solution treated b) after 1st step of aging and c) after 2nd steps of aging

Figure 5 and 6 show the relationship between flow stress on deformation

temperature and strain rate, respectively. The classic interdependence of the flow

stress and deformation parameters can be seen, namely: the flow stress increased

with decreasing deformation temperature and increasing strain rate. This

behaviour is similar to the results obtained by Guimaraes and Jonas [5].

In the present work, activation energy of deformed superalloy was

determined in the way: the steady state stress values evaluated from flow stress

obtained within the range of 1000-1200°C were plotted as a function of inverse

temperature and the logarithm of strain rate lnσmax = f(1/T) and lnσpl = f(ln

).

This gives the relationship between the peak strain and steady state stress and

strain rate at constant temperature.

a) b)

c)


Fig. 6. Relationship between the flow stress and strain rate for CMSX4: a) solution treated,

b) after 1st step of aging and c) after 2nd steps of aging

The activation energy of deformation was then determined from the slopes

of these curves. The values of 1

ln

T

;

ln

ln T

were used to estimate the

activation energy for high-temperature deformation process of the investigated

nickel based alloy. For the range of deformation conditions employed, flow

stress as a function of deformation temperature and strain rate was analysed

using a hyperbolic-sine Arrhenius type equation [6].

Flow stress vs. deformation temperature and strain rate dependence

σpl = f( ,

T) was determined based upon both literature equations and

experimental data (Fig. 4 and 5).

Activation energy Q for the deformation process of CMXS4 is strongly

affected by temperature and strain rate (Table 1).

The mean value of activation energy for high-temperature forming in the

temperature range of 1000-1200°C is for CMSX-4 equal to 779,46 kJ/mol.

Estimated value of activation energy (Q) has a physical meaning and can be used

in practice for modelling many types of engineering processes, e.g. analysis of

plastic forming using the Finite Element Method.

Flow stress vs. deformation temperature and strain rate dependence

σpl = f( ,

T) was determined based upon both equations (1), (2), (4) and

experimental data (Figs. 5 and 6).

14 2,343.09 10 [sinh( )] expQ

xRT

(10)

Activation energy Q for the deformation process of CMSX-4 is strongly affected

by temperature and strain rate (Table 1).


Table 1. Activation energy for the CMSX-4 deformed in the temperature range of 1000-1200°C

Strain rate

, s-1

Temperature, °C

1000 1050 1100 1150 1200

Activation energy Q, kJ/mol

10-4

Solution Heat Treated CMSX-4

741 - 786 828 911

CMSX-4 after S1 aging

749 784 796 824 841


755 794 816 834 794

4x10-4

Solution Heat Treated CMSX-4

689 - 732 771 848


697 730 741 783 802


703 738 760 777 801

The mean value of activation energy for high-temperature forming of in the

temperature range of 1000-1200°C is for CMSX-4 = 779,46 kJ/mol. Estimated

value of activation energy (Q) has a physical meaning and can be used

in practice for modeling many types of engineering processes, e.g. analysis

of plastic forming using the Finite Element Method. The effect of deformation

temperature and strain rate on the flow stress can be expressed by the Zener-

Hollomon parameter Z. Figure 7 shows relationship between the flow stress and

the Z parameter. The flow stress value increased with increasing the Z

parameter.


Fig. 7. Relationship between flow stress and the Z parameter for deformed

of solution treated CMSX-4

3. Discussion

True stress-true strain curves (Fig. 2-4) confirmed, that increasing

deformation temperature, or strain rate decreasing result in decreasing of flow

stress value σpl. Decreasing the value of strain rate by eight (from 4x10–4

to

10–4

s–1

) results in a 15% flow stress reduction. Increase of deformation

temperature was found to have a greater influence on the flow stress value

reduction. One must notice two distinguishable regions on the flow stress curves

of the heat treated samples deformed at relatively lower temperatures, namely:

1000 and 1050°C and with strain rate of 10–4

s–1

. The first region, which occurs

at an applied strain not exceeding 0.05, is characterized by almost uniform work

hardening to a hump due to effective static precipitation within the alloy. The

second region is characterized by a rapid flow softening followed by sample

fracture at strain not exceeded the value of ε ≈ 0.1. However, the flow stress of

the samples deformed at these temperatures with higher strain rate (4x10–4

s–1

)

increased to a peak value and then rapidly decreased as the strain further

increased.

Basing on the diagrams – Fig. 5 and 6, the factors were determined in order

to estimate the mean value of activation energy (Q) of high-temperature

deformation process of examined alloy – Q = 779,46 kJ/mol. The results (Table

1) show that activation energy depends on temperature and strain rate.

Analogous dependence of deformation parameters on the value of activation

energy was observed in other alloys systems and metals [4, 6]. One cannot,

however, generalize in respect to the strain rate and temperature, the tendency in

the change of activation energy for all type of materials. It is worth to emphasize

that any particular single structural process could not be ascribed to the value of

energy activation. Change of fraction of thermally activated dynamic recovery

process and dynamic recrystallization in depreciation of the flow stress value is

due to variation of the deformation parameters. It would be almost impossible to

draw distinction between this processes on the grounds of an energy activation

value. Therefore, averaging Q values obtained from the deformation within wide

temperature and strain rate range should be treated as a mathematical treatment

allowing to determine on of a constant in the equation describing the relationship

between deformation parameters and flow stress value.

The results of high-temperature deformation of the examined CMSX4 alloy

may possibly find some practical use in the workshop practice to predict a flow

stress values, but only within particular temperature and strain rate ranges.

Dissimilar energy activation values obtained under various conditions

(depending on a research centre) or for a variety of materials make impossible to


do a direct comparison of measurements, e.g. by means of plotting them on one

common graph pl = f(Z).

Acknowledgements

The authors would like to thank Polish Ministry of Science and Higher Education

for its financial support – this work was carried out under grant No. N N507 300640.

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Received in August 2014

STRESS STRAIN CURVES UNDER COMPRESSION FOR CMSX4...

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